The Ebola virus disease is a severe viral haemorrhagic fever syndrome caused by Ebola virus. This disease is transmitted by direct contact with the body fluids of an infected person and objects contaminated with virus or infected animals, with a death rate close to 90% in humans. Recently, some mathematical models have been presented to analyse the spread of the 2014 Ebola outbreak in West Africa. In this paper, we introduce vaccination of the susceptible population with the aim of controlling the spread of the disease and analyse two optimal control problems related with the transmission of Ebola disease with vaccination. Firstly, we consider the case where the total number of available vaccines in a fixed period of time is limited. Secondly, we analyse the situation where there is a limited supply of vaccines at each instant of time for a fixed interval of time. The optimal control problems have been solved analytically. Finally, we have performed a number of numerical simulations in order to compare the models with vaccination and the model without vaccination, which has recently been shown to fit the real data. Three vaccination scenarios have been considered for our numerical simulations, namely: unlimited supply of vaccines; limited total number of vaccines; and limited supply of vaccines at each instant of time.

Figure 2.
(a) Cumulative confirmed cases: in dashed circle line the real data from WHO and in continuous line the values of $I(t) + R(t) + D(t) + H(t) + B(t) + C(t) - \mu(N - S(t) - E(t))$ from (1) with the parameter values from Table 1. (b) Cumulative confirmed cases given in (2), when available an unlimited supply of vaccines, also with the parameter values from Table 1

Figure 3.
Individuals $S(t)$, $E(t)$, $I(t)$ and $R(t)$. In dashed line, the case of vaccination without limit on the supply of vaccines; in continuous line, the case with no vaccination with the parameter values from Table 1

Figure 4.
Individuals $D(t)$, $H(t)$, $B(t)$ and $C(t)$, with the parameter values from Table 1. In dashed line, the case of vaccination without limit on the supply of vaccines; in continuous line, the case of no vaccination